The Muppet’s Guide to: The Structure and Dynamics of Solids 5. Crystal Growth II and Defects

Crystal Growth All growth processes require conditions that promote formation of a crystal such as: –Condensing from a supersaturated solution –Freezing from a melt –Evaporation Different methods needed for different materials

-adatom Crystal growth happens at steps (001) (111) (101) (011) 5μm5μm CdTe in N 2

Ce 0.5 Zr 0.5 O 2 Figures adapted from W.D. McAllister, Materials Science and Engineering, 7 th edition, Wiley. Figures after M. Boudart Kinetics of Heterogeneous Catalytic Reactions, Princeton University Press,1984 and W.J. Stark et al. Chem Comm (2003)

-Impurity species -adatom Blocking of step flow by impurities Cohesive energy, E c

Growth from Solution Evaporation of the solvent causes super-saturation and hence the solute comes out of solution

Growth from the melt Czochralski growth –Liquid encapsulated Czochralski growth Bridgman growth (directional freezing) –Interface shape –Thermal considerations

Czochralski growth (crystal pulling) A seed is lowered into the melt The seed is rotated and withdrawn

Czochralski growth (crystal pulling)

A seed is lowered into the melt The seed is rotated and withdrawn A rod or boule of crystal forms Industry standard for Si and Ge Pure Material Melt + Impurities

Czochralski growth A seed is lowered into the melt The seed is rotated and withdrawn A rod or boule of crystal forms Industry standard for Si and Ge "Smithsonian", Jan 2000, Vol 30, No. 10

Liquid encapsulated Czochralski growth Growth takes place in a pressure vessel The melt is covered in boric oxide (B 2 O 3 ) which is viscous and un-reactive This allows an over- pressure of inert gas to be applied so as to contain the melt – important for GaAs and CdTe (volatile components)

Bridgman growth Boat is moved through the temperature gradient in a tube furnace Growth of the crystal is by directional freezing of the melt T x solidliquid

Directional freezing Material is contained in a capsule A concave growth surface allows secondary nuclei to form at the walls of the tube A convex growth surface causes secondary nuclei to be crowded out by the main crystal in the advancing solid Freezing direction, x solid liquid solid liquid

Hot Zone or Float Zone Crucible free growth or anneal Also used to remove impurities

Impurities Segregation coefficient: For k<1, impurities stay in melt Diffusion mechanism

Layer by Layer Growth For epitaxial growth we want the layer to stick: Energy to remain on surface, E a Energy to diffuse on surface, E d Cohesive energy, E c Strain Energy, (U)

1<θ<2 M L θ<1 M L θ>2 M L Layer by layer or Frank-van der Merwe Mode Layer plus island or Stranski-Krastanov mode Island or Volmer-Weber mode Thin film Growth Modes Growth mode depends on energies when atoms arrive at substrate

Epitaxial growth Molecular beam epitaxy Co-evaporation of the elements that make the compound at UHV Base pressure of chamber < Torr. Growth pressure <10 -9 Torr

Sputtering Base pressure of system <10 -7 Torr. Growth in Ar <10 -3 Torr

Heterostructures

Lattice Match through Rotations Pt[100]//FeCo[110] 45° Rotation of unit cells a Pt =3.9242Å a Fe =2.8665Å

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Disorder in crystalline materials No such thing as a perfectly ordered material Many materials are technologically of value because they are disordered/imperfect in some way: silicon devices – controlled levels of deliberate impurity additions (ppb)p-type : BSi  B + h n-type : PSi  P + e steels – additions of 0.1 to 1 at.% other metals to improve mechanical properties and corrosion resistance

Vacancy atoms Interstitial atoms Substitutional atoms Point defects Types of Imperfections Dislocations Line defects Grain Boundaries Area defects

Imperfections in Solids Linear Defects (Dislocations) –Are one-dimensional defects around which atoms are misaligned Edge dislocation: –extra half-plane of atoms inserted in a crystal structure –b  to dislocation line Screw dislocation: –spiral planar ramp resulting from shear deformation –b  to dislocation line Burger’s vector, b: measure of lattice distortion

Dislocations – linear defects Source: -growth -stress -temperature Evidence: -metals more deformable than predicted (but can be strengthened by impurities) -spiral growths on surface of some crystals -reactions occur at active surface sites Types: edge, screw, intermediate Transmission electron micrograph of Ti alloy – dark lines are dislocations (Callister: Materials Science and Engineering)

Edge dislocation – partial plane of atoms – lattice distorted where plane ends Dislocations characterised by the Burgers vector, b -for metals, b points in a close-packed direction and equals the interatomic spacing (Callister: Materials Science and Engineering)

Heterostructures ┬

Buffer Layers ┬ ┬ ┬

Screw dislocation partial slip of a crystal on one side of dislocation line, crystal has undergone slip; on other side, crystal is normal continued application of shear stress causes dislocation to move through crystal Shear stress (Callister: Materials Science and Engineering)

Edge, Screw, and Mixed Dislocations Edge Screw Mixed (Callister: Materials Science and Engineering)

Interfacial (planar) defects boundaries separating regions of different crystal structure or crystallographic orientation –External surfaces (see final section of module) –Internal boundaries Layer Interfaces (2D) Region Interfaces (3D)

Freezing - result of casting of molten material –2 steps Nuclei form Nuclei grow to form crystals Crystals grow until they meet each other –grain structure Planar Defects in Solids nuclei crystals growing grain structure liquid (Callister: Materials Science and Engineering)

Polycrystalline Materials Grain Boundaries regions between crystals transition from lattice of one region to that of the other slightly disordered low density in grain boundaries – high mobility – high diffusivity – high chemical reactivity Adapted from Fig. 4.7, Callister 7e.

Grain boundaries D = b/  b Internal surfaces of a single crystal where ideal domains (mosaic) meet with some misalignment: high-angle and small(low)-angle. NB – in polycrystalline materials, grain boundaries are more extensive and may even separate different phases Small-angle grain boundary equivalent to linear array of edge dislocations bonding not fully satisfied  region of higher energy, more reactive, impurities present. (Callister: Materials Science and Engineering)

Planar Defects in Solids 2 Another case is a twin boundary (plane) –Essentially a reflection of atom positions across the twin plane. Stacking faults –For FCC metals an error in ABCABC packing sequence –Ex: ABCABABC (Callister: Materials Science and Engineering)